Breeding
There are 13 "Egg Groups" for Pokemon, with some belonging to multiple groups. To create Pokemon eggs, you must use two opposite-gendered Pokemon from the same egg group. You can also use the Pokemon Ditto with any other Pokemon, but it will take slightly longer for any such pairing to produce an egg. To determine how long it will take to create an egg, ask the Daycare Owner how your Pokemon are doing. If he says, "The two don't seem to like each other," the pair may not produce an egg at all, or it will take the longest amount of time. The response "The two seem to get along" means it shouldn't take long and "The two seem to get along very well!" means the egg will arrive soon.
"Baby" Pokemon
If you breed certain Pokemon holding items, you can create eggs that contain "Baby" Pokemon or a pre-evolved form of that Pokemon. An example is Munchlax, the pre-evolution of Snorlax. The only way to obtain Munchlax is to breed two Snorlax, with one holding a "Full Incense." Seventeen Pokemon can only be obtained through breeding. As of 2011, a complete list of these Pokemon and their needed items is available at Pokemon-centric websites such as Serebii or Psypokes.
Hatching Eggs
Once you have received an egg, walk around with it to hatch it. Depending on the egg, this can take anywhere from 1,000 to 10,000 steps. If you ride a bike, it will take much less time. If you have a Pokemon with the "Flame Body" ability, the amount of steps will be cut in half.
Masuda Method
A "shiny" Pokemon is so rare that the chance of breeding one the normal way is 1 in 8,192. These odds drop to 1 in 2,048 using the "Masuda" method," which requires you to use Pokemon pairs from different countries to produce the egg. Pokemon from different countries are available through the online Global Trading Station.